Lattice of soft topologies
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In a machine learning environment involving inferential knowledge derived from the association between causes and effects, soft set theory can be employed effectively. In the present paper we study about the set of all soft points on a given universal set and a set of parameters. The relation between this set and the set of all soft sets on a given universal set was investigated. Given a universal set and a set of parameters, it is established that there is a bijection between the family of all topologies on the set of all soft points and the family of all soft topologies. It is also proved that the family of all soft topologies is a complete lattice and the bijection mentioned above is a lattice isomorphism.
Abstract
In a machine learning environment involving inferential knowledge derived from the association between causes and effects, soft set theory can be employed effectively. In the present paper we study about the set of all soft points on a given universal set and a set of parameters. The relation between this set and the set of all soft sets on a given universal set was investigated. Given a universal set and a set of parameters, it is established that there is a bijection between the family of all topologies on the set of all soft points and the family of all soft topologies. It is also proved that the family of all soft topologies is a complete lattice and the bijection mentioned above is a lattice isomorphism.
참고문헌 (19)
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